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Current capacity of multi-strand versus single-strand

Discussion in 'Electronic Basics' started by Zarbol Tsar, Dec 3, 2004.

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  1. Zarbol Tsar

    Zarbol Tsar Guest

    Would a multi-strand flexible wire have the same current carrying
    capacity as a solid single stranded cable of the same cross section.

    For example ... a multi-strand with a cross section for its wire
    portion of 0.75 mm squared and a single strand cable also of 0.75 mm
  2. Any particular frequency in mind?

    Skin effect is the obvious thing that will make a stranded wire better
    than a solid of the same csa. But this kicks in at higher frequencies.

    Here is a brief simplified guide:

    However, if the actual csa of the solid wire is compared with actual csa
    of the stranded wire (rather than the sum of the csa of individual
    strands), then a solid wire will have more copper and hence lower
    resistance. This is frequency independent.

    So, at low frequencies or DC, a solid wire of the same core diameter
    will be better than stranded. As frequency rises, a point will come
    where stranded wire will be better; it will be able to take a higher
    current than a solid core of the same diameter.

    There are obviously exceptions.

    Hope that is what you were after...
  3. Tim Williams

    Tim Williams Guest

    Ya, until you get into higher frequencies where the slightly greater surface
    area of the stranded wire represents more cross section. Probably above

  4. Skin effect is easily measurable at a few tens of kHz.
    It comes into effect at regular mains frequences for very large
    conductors. An alternative to making them stranded is to pick
    a different shape which avoids significant depth of metal,
    such as a flat strip (thin rectangular profile), or tubular.
  5. In most cases, they are exactly the same. When the frequency gets
    high enough that skin effect starts to crowd the current toward the
    surface, stranded wire has a slight advantage, but this is greatly
    enhanced if all the strands are insulated from each other (look up
    litz wire). This effect can also be used ot advantage when winding
    magnetic devices with enameled wire, and two or more parallel strands
    can be used in place of an equivalent cross section single wire. But
    for ordinary hook up wire, they are usually assumed to have an
    ampacity based on their cross sectional area, not the number of
  6. A No, 12 AWG wire has a diameter of 0.78 mm.

    For wire sizes 2.47 mm and under (No. 2 AWG and under) the DC resistance
    nearly equals AC resistance. Therefore the ampacity for stranded conductors
    is nearly equal to that for solid conductors for these small conductors
    (also demonstrated using the N-M equations.) For building wire types,
    conductors size No. 8 AWG and larger that are installed in raceways are
    required to be stranded (NEC Section 310.3.) Therefore, we seldom see
    conductors larger than No. 8 that are solid, except for the No. 4 bare
    grounding conductors carried on line trucks and sold for services by supply
    houses that are used as grounding electrode conductors so that no additional
    protection is required. The standard ampacity table in the NEC used for
    building wires, 310.16, does not distinguish between solid and stranded
    conductors. This is probably because almost all building wire No. 8 and
    larger is stranded.
    The N-M equations also do not distinguish between solid and stranded, but
    uses DC resistance multiplied by (1+YC) where YC becomes measurable for
    wire sizes above No. 2 because of skin effect.
  7. For No. 12 AWG Table 8 of the NEC does list two different DC resistances for
    stranded and solid copper.

    DC resistance per 1000 feet for solid is 1.93 ohms

    For stranded the DC resistance is given as 1.98 ohms per 1000 feet.

    So solid should have a slightly higher ampacity.

    If we use Table 310.16 of the NEC to determine RCA and substitute into the
    Ampere calculation we can find the approximate differences in ampacity.

    From Table 310.16 using 75 degrees C as the ambient.

    I = 25 amperes, TC = 75 degrees C, and TA = 30 degrees C and RDC = 1.98 ohms
    per 1000 feet or 0.00198 ohms per foot.

    This converts to 1980 microhms.

    From I (in kiloamperes) = SQRT(( TC-TA)/RDC*RCA))



    Or RCA = (75-30)/1980*0.025*0.025

    RCA = 36 thermal ohm feet

    For stranded, I = 0.025 kiloamperes from the table

    For solid No. 12 copper

    I (in kiloamperes) = SQRT ((75-30)/1930*36)

    or I = 0.0254 kiloamperes

    Then the solid No. 12 copper would have a 0 .4 ampere increase in ampacity.

    This is a 0.4/25 *100 or only a 1.6 per cent increase.

    Considering that ampacity tables are approximations, this increase in
    ampacity does not exceed the error of approximation.
  8. Tom Biasi

    Tom Biasi Guest

    If indeed the conducting areas are the same the capacity will be the same
    for all practical purposes.
    The AWG (American Wire Gauge) numbers take into account the actual total
    cross-sectional area.
    Some charts will compare stranded vs. solid for actual wire outer diameter
    If you start talking about impedance in some applications the story will
  9. Rowbotth

    Rowbotth Guest

    As far as I am aware, the amount of copper being the same should mean
    the same current flow - but the more strands should mean it is easier to
    work with, albeit more expensive?

  10. I just reviewed the Samuel Rosch Paper from 1938, "The Current Carrying
    Capacity of Rubber-Insulated Conductors."
    He used a slightly different formula where N represented the number of
    current carrying conductors. Since Table 310.16 is for three current
    carrying conductors in a raceway to find RCA the following should be used:

    I (in kiloamperes) = SQRT(( TC-TA)/N*RDC*RCA))
    RCA = (75-30)/3*1980*0.025*0.025
    RCA= 12 Thermal Ohm Feet

    Then for solid No. 12 AWG copper:
    I (in kiloamperes) = SQRT ((75-30)/3*1930*12)
    I = 0.0254 kiloamperes

    And there is no difference in the answer.
  11. I should also note that Samuel Rosch did his calculation for an ambient of
    30 degrees C and TC = 50 degrees.
    He came up with the following ampacity table for copper (only sizes up to
    No. 2 are shown):

    Wire Size - Amperes
    14 - 15
    12 - 19
    10 - 26
    8 - 35
    6 - 47
    4 - 61
    2 - 78
    To convert these values to ampaeres for a TC (insulation temperature) equal
    to 75 degrees C. We need to derive an equation:
    Let I1 equal ampacity for 50 degree insulation and I2 equal ampacity for 75
    degree insulation,
    I1 (in kiloamperes) = SQRT(( TC1-TA)/N*RDC1*RCA))
    I2 (in kiloamperes) = SQRT(( TC2-TA)/N*RDC2*RCA))
    Where TA = 30 degrees C.
    and RCA is equal in both equations.
    RDC1 is DC resistance in microhms at 50 degrees C
    RDC2 is DC resistance in microhms at 75 degrees C.
    TC1 = 50 degrees C.
    TC2 = 75 degrees C.
    Using the proportionality rule where two ratios that are equal can be cross
    I2*(SQRT(( TC1-TA)/N*RDC1*RCA))) = I1*(SQRT(( TC2-TA)/N*RDC2*RCA)))
    and squaring both sides:
    I2*I2*(( TC1-TA)/N*RDC1*RCA)) = I1*I1*(( TC2-TA)/N*RDC2*RCA))
    I2*I2 = (I1*I1*(( TC2-TA)/N*RDC2*RCA))) / (( TC1-TA)/N*RDC1*RCA))
    I2*I2 = I1*I1*( TC2-TA) * RDC1/ ( TC1-TA) * RDC2
    I2 = I1* SQRT (( TC2-TA) * RDC1 / ( TC1-TA) * RDC2)

    Next we use the N-M equation for finding DC resistance:

    rdc = ohms
    pc = circular mil ohms per foot of conductor at 20 degrees C. (10.371 ohms
    for 100% IACS copper, 17.002 ohms for 61% IACS aluminum)
    tah = absolute value of inferred temperature of zero resistance. (234.5
    degrees C. for copper and 228.1 degrees C. for aluminum)
    cma = circular mil area of conductor from Chapter 9 Table 8 of NEC
    tc = conductor temperature in degrees C.

    At 50 degrees C.
    RDC1 = (1.02 * 10.371 / CMA) * (234.5 + 50) / (234.5 + 20)
    At 75 degrees C.
    RDC2=(1.02 * 10.371 / CMA) * (234.5 + 75) / (234.5 + 20)

    If we feed this into a spreadsheet we come up with the following ampacity
    table for TC = 75 degrees C.
    We get the following table:
    Wire size - amperes
    14 - 21
    12 - 27
    10 - 37
    8 - 50
    6 - 67
    4 - 88
    2 - 112
    If we round these to the nearest 5 amperes:
    14 - 20
    12 - 25
    10 - 35
    8 - 50
    6 - 65
    4 - 90
    2 - 110
    How do these compare to table 310.16?
    wire size - calculated amperes - Table 310.16

    14 - 20 - 20
    12 - 25 - 25
    10 - 35 - 35
    8 - 50 - 50
    6 - 65 - 65
    4 - 90 - 85
    2 - 110 - 115

    This shows that Table 310.16 in the NEC has a general round off error that
    exceeds the difference in ampacities between solid and stranded conductors
    (at 60 Hz) for small wire sizes.
  12. In very high voltages, 400 kV and over, it's not the same due to corona
    effect (ionization of the air around the conductor).So, the utility puts two
    conductors in parallel.That's the only example I can think of;in every day
    applications it has no meaning.
  13. What I mentioned before, is actually the strength of the electric field
    around the conductor, that is reduced by the use of two (conductors) and
    ionizes the air, making a noise like humming bees.
  14. Here, we use the following gauges (in residence and small industry):1.5,
    2.5, 4, 6, 10 mm^2.The former 3 are stranded or solid, the latter 2 always
    stranded.It's very difficult to bend the thick wires when they are solid, so
    they stopped producing solid 10 mm^2 wires, used to wire old-fashioned fuses
    and circuit breakers.The ampacity of these conductors is 10,16,20,25,35
    amperes respectively and should be properly fused, according to local rules,
    with circuit breakers.Actually, the max.current of a copper wire depends on
    the max.allowed temperature, hence whether the insulation is PVC or
    something else (usually PVC here).All formulas have the gauge in mm^2 here,
    my book says nothing about the mentioned issue, maybe it's different in USA.
    the voltage drop in a (loaded) cable is:
    ÄU/U=2 I Ø' I cos ö /U
    (the greek letters are delta, psi and phi respectively)
  15. Are your areas the total area of stranded or solid or are they the combined
    area of the copper only.
    We use Circular Mil Area (CMA) to define the copper area.

    CMA is the diameter of a conductor in thousandths of an inch squared and
    represents the total copper area.
    For instance, a No. 12 AWG has a CMA equal to 6530 for both stranded and
    solid No. 12 conductors, but the cross sectional areas are different.
    The cross sectional area of a solid No. 12 is 3.31 MM^2 and 4.25 mm^2 for
    stranded. Cross sectional areas do little for calculating ampacity.
    We use CMA because resistance is inversely proportional to CMA because CMA
    represents actual copper.
    Also you give your ampacities, but what maximum operating temperature are
    these for and what is the ambient temperature?
    Also, are your ampacities for in cable, 3 conductors in raceway, etc.
  16. Don Kelly

    Don Kelly Guest

    Utilities use bundled conductors at lower that 400KV. The main reasons for
    this is to
    a)make construction easier and cheaper
    b)reduce the series inductance of the line
    c) reduce conductor surface fields and corona.
    So you have hit one reason out of three.
  17. That means I am not passing the exam?
  18. The ampacities are for normal conditions, thus residence.It's a thumb rule
    which cable to use for what load.A cooking range needs 6 mm^2, a water
    heater 4 mm^2, a washing machine and dishwasher and most space heaters 2.5
    mm^2 and incadescent lighting 1.5 mm^2.I suppose these calculations are for
    the climate of Greece, and for three wires (live, neutral, earth) in a
  19. Area of the copper only, in Europe.
    Answering for the UK...

    Assumes ambient of 30ºC and maximum operating temperature of 70ºC.
    For ambient temperatures above 30ºC, max current is reduced by
    tables, and reaches zero at 70ºC. Circuit protection for overload
    and fault current conditions is designed to prevent cable exceeding
    160ºC during a fault or overload (i.e. a maximum 90ºC temperature
    rise from operating temperature), or it would be permanantly
    damaged and need replacing. Higher temperature cable is available
    for situations which require it.
    We have different maximum ampacities for a number of different
    installation methods. The highest is for a cable in a cable tray,
    going through to the lowest which is for a cable embedded in a
    thermally insulating wall. We also have 'grouping factor' which
    reduces the ratings of multiple cables when closely spaced.
  20. "Normal conditions" is a broad term. In the USA the NEC (National
    Electrical Code) has many specifics for ampacity tables. For instance, the
    main Table 310.16 that we use for building wire ampacity defines the ambient
    as 30 degrees C. and has derating factors where the temperature exceeds this
    for long runs. If the temperature is excessive for no more than 10 per cent
    of the circuit length to a maximum of ten feet whichever is less, then no
    excessive temperature derating is required. The ampacities are also defined
    for no more than three current carrying conductors in a raceway or cable.
    If conductors are bundled or cables with more than three current carrying
    conductors are bundled for longer than 24 inches or if there are more than
    three current carrying conductors in a raceway or cable there are additional
    derating factors. In some cases where there is excessive temperatures and
    more than three current carrying conductors double derating is required. We
    also have a rule for continuous loads requiring a 80 per cent derating.
    There are also rules defining a current carrying conductor. If a neutral
    only carries unbalanced current it is not counted as a current carrying
    conductor. But where the majority of current in a neutral is from discharge
    lighting, third harmonics, or computer loads it is counted. Also, the
    grounding conductor is not counted as a current carrying conductor. Also,
    ampacities are listed for three temperatures for copper and for aluminum.
    One column is for 60 degrees insulation, one for 75 degrees C. and one
    column for 90 degree C. The maximum operating temperature of a conductor
    cannot exceed the maximum allowed rated operating temperature for the
    terminals, equipment or insulation whichever is the lesser. We can use the
    90 degree column for derating purposes. For example if there are 9 No. 12
    AWG (American Wire Gauge) 90 degree C. rated current carrying conductors in
    a raceway we can multiply the derating factor of .7 times the 90 degree
    ampacity of 30 amperes to get 21 amperes and use this as the ampacity but
    other rules still apply. Our rules are so complicated that it took me about
    5 weeks to write an Excel program to determine ampacity. This program is
    accessible at
    But in general for dwelling units (where people live, eat, sanitize, and
    sleep), we use No. 8 AWG copper on a two pole 40 ampere circuit breaker for
    ranges, No. 10 AWG copper on a two pole 30 ampere circuit breaker for hot
    water heaters, and No. 12 AWG copper on single pole 20 ampere circuit
    breakers for general purpose lighting and appliance circuits.
    The NFPA (National Fire Protection Association) that writes the NEC wants
    the international community to adopt the NEC as an International Electrical
    So you too may become acquainted with our famous NEC someday!
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